Chord is one of the simplest peer-to-peer systems that addresses the issue of efficient data location. Despite its simplicity, one of its main limitations remains the asymmetric organization of its routing. This leads to problems like inability to make in-place notifications of routing entry changes, and incapacity to support symmetric applications and to efficiently exploit network proximity. As a solution to this limitation, we propose S-Chord, an extension to Chord. In S-Chord the routing is organized in a symmetric manner, and the circular search space can be walked through bidirectionally. This results, for the worst-case, in an improvement of lookup efficiency of 25%, compared to Chord with the same size routing table. Furthermore, on average, assuming a uniform distribution of queries, S-Chord results in a 10% improvement. To test our theoretical results we implemented the S-Chord lookup algorithm and applied it to different networks.